Precrystallization clusters of holoferritin and apoferritin at low temperature

S. Boutet* and I. K. Robinson†

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA�Received 29 September 2005; revised manuscript received 2 January 2007; published 21 February 2007�

The formation of small nanosized clusters of the proteins holoferritin and apoferritin at low temperature wasstudied using small angle x-ray scattering. A strikingly large temperature dependence for the average molecularspacing in the clusters was observed. Calculations of the scattered intensity for various cluster models wereperformed. Comparison of the data with the simulations revealed the presence of crystalline order in theclusters of size ranging from a few molecules to a few hundred molecules. The crystalline order was found tobe preserved with the lattice spacing varying with temperature by up to 20%. The small clusters were observedto grow into large micron-sized crystals when they were annealed and under certain conditions, the smallclusters were found to coexist with the large crystals. This suggests that these clusters are closely related tocritical nucleation. The data are consistent with an isotropic nucleation pathway, but cannot completely rule outa smaller presence of planar nucleation.

DOI: 10.1103/PhysRevE.75.021913 PACS number�s�: 87.15.Nn, 61.10.Eq, 87.64.Bx, 81.10.�h

I. INTRODUCTION

The standard method to determine the atomic structure ofbiological macromolecules such as proteins is crystallogra-phy in which a crystal of the macromolecule is preparedusing some standard techniques �1�. This crystal is irradiatedby an x-ray beam, the diffraction pattern is measured andthen inverted to obtain a three-dimensional atomic structure.Much of the difficulty in the process lies in obtaining goodquality crystals which diffract well enough at atomic resolu-tion. For many known proteins, attempts to find conditionswhich will yield crystals have failed. The search for crystal-lization conditions is generally carried out by trial and errorresulting in painstaking and sometime unsuccessful work.

For this reason, it is worthwhile to study the protein crys-tallization process itself in order to understand what causessome proteins to crystallize while others do not. Also, thereis hope that such studies can provide some kind of ability topredict which proteins will crystallize and under which con-ditions they are likely to do so �2,3�.

There are two distinct stages in the crystal formation pro-cess. The first one is known as the nucleation process inwhich stable aggregates of proteins form from a saturatedsolution �4–6�. The second stage is called the growth pro-cess. It is during this latter process that the stable nuclei growinto large crystals, often by adding layers upon layers to thecrystal �7,8�.

The nucleation process is the less well understood of thetwo and the one generally thought to be responsible for theexistence or nonexistence of crystals. Crystals cannot grow ifthere are no stable initial aggregates formed onto which otherproteins can leave solution and attach to. Crystals are alsoprevented from growing when the nucleus is a noncrystallineaggregate. The stable nanocrystalline aggregates are calledcritical nuclei because when they reach a certain size, theybecome more likely to grow than they are likely to redis-

solve. The size of the critical nuclei depends on the proteinand also on the level of supersaturation of the solution �1�.They range from very small �a few molecules� at high satu-ration to infinite for solutions below saturation. In the usualcase where one wants to produce a few large high qualitycrystals in a few days, the level of supersaturation needs tobe adjusted in such a way that only a few critical nuclei areformed over this period. It is then very difficult to studycritical nuclei because of their rare occurrence. Once formed,however, they should be of a size large enough to study withsome standard techniques such as AFM �9�. However, thosenuclei are floating around in solution which makes them vis-ible to the AFM only when they attach to an existing sub-strate such as a large crystal. Observing isolated nuclei insolution as they form is very difficult.

One possible technique to study protein nucleation is co-herent x-ray diffraction �CXD� �10,11�. which allows themeasurement of a complete diffraction pattern of a crystal-line nanoparticle. This diffraction pattern can be inverted toyield the complete shape and internal structure of the par-ticle. CXD should allow the study of isolated critical nucleiof size below 1 �m. It is currently difficult to perform suchexperiments since they are limited by x-ray flux, detectorspeed, and radiation damage.

During an attempt at performing one of those CXD ex-periments, a solution containing thousands of micron sizedcrystals of the protein ferritin in equilibrium with the solu-tion phase was frozen in order to try to mitigate the effects ofradiation damage as well as slow down the motions of thecrystals in solution. A new aggregated state of ferritin wasfound to exist, as was previously reported by Kilcoyne et al.�12�.

In this paper we investigate this freezing transition andrelate the frozen state to nucleation. The samples and tech-niques used for the measurements are first detailed in Sec. II.The scattering results obtained with the protein holoferritinare then presented in Sec. III along with how the scatteredintensity and structure factors vary with temperature and pro-tein concentration of the solution. In Sec. IV, we presentsimilar results for apoferritin solutions. Simulations of thescattering structure factors of small isotropic and planar clus-

*Electronic address: sboutet@slac.stanford.edu†Electronic address: i.robinson@ucl.ac.uk

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ters of various size are presented in Sec. V. Section VI dis-cusses the fitting of the measured patterns to the simulatedones and finally Sec. VII discusses how the results relate tonucleation.

II. SAMPLE AND EXPERIMENTAL METHOD

The protein ferritin extracted from horse spleen was ob-tained from the Sigma-Aldrich Company. It is composed of24 subunits arranged in a 432 symmetry forming a sphericalshell of inner diameter �80 Å, outer diameter �130 Å, andMWt=474 000. It has the biological function of storing ironas ferrihydrite in its cavity and releasing it when it is neededby the organism �13�. It readily crystallizes into the facecentered cubic �fcc� lattice with lattice parameter a=183 Åwhen cadmium salt is added. Two Cd2+ ions form saltbridges at every twofold axis of the protein �14�. Both theiron filled protein �holoferritin or sometimes called simplyferritin� and the empty shell �apoferritin� were studied. Ho-loferritin was obtained at a concentration of 100 mg/ml in150 mM NaCl while apoferritin was obtained at a concentra-tion of 50 mg/ml in 100 mM NaCl. Holoferritin is about55% more massive than apoferritin due to the presence ofiron. Solutions containing a higher concentration of proteinswere obtained by filtering through an Amicon Ultra 10 000MWCO centrifugal filter from Milipore.

Solutions of ferritin were placed, as bought, inside x-rayquartz capillaries of diameter 1 mm. The capillaries wereglued using thermal paste to a Peltier cooling device whichwas mounted on a water-chilled copper block serving as aheat sink. This setup allowed the temperature of the sampleto be varied from 15 to −35 °C. A K-type thermocouple wasused to measure the temperature of the sample.

The samples were placed into the x-ray beam at Sector34-ID-C at the Advanced Photon Source �APS� at ArgonneNational Laboratory. The small angle x-ray scattering�SAXS� patterns from the samples were collected using adirect-read CCD camera from Roper Scientific placed atvarious distances from the sample. The x-ray energy fromthe undulator was set to 9 keV and further monochromatizedusing a double crystal Si�111� monochromator. Beam-defining slits of 200�200 �m2 were used 1 m upstream ofthe sample with cleanup slits 10 mm upstream of the sample.

III. HOLOFERRITIN RESULTS

The SAXS pattern observed from a solution of iron-loaded ferritin at room temperature shows a monotonic de-crease in intensity versus momentum transfer �q=4� sin�� /2� /��, where � is the scattering angle and � is thewavelength of the x rays. This is due to the fact that the ironcore varies in size and shape from molecule to molecule.There are no observable features such as oscillations in theSAXS pattern due to the incoherent summation of diffractionpatterns from effectively different molecules. On the otherhand, apoferritin molecules are all identical and have aroughly spherically symmetric structure giving rise toBessel-like function oscillations in the SAXS data �15�. Thedifference between holoferritin and apoferritin can be seen in

Figs. 1�a� and 1�b�. Also shown in Fig. 1�c� is the SAXS datafrom ferritin to which was added 90 mM CdCl2 salt whichwas found to produce a shower of micron-sized crystals.Sharp rings of intensity can be seen as expected from a pow-der diffraction pattern. The Bragg peaks seen are the �111�,�200�, and �220�, the first three peaks expected from an fcccrystal of ferritin. Figure 1�d� shows what happens to a so-lution of holoferritin when it is frozen to −20 °C. The con-tinuously decreasing intensity with q is replaced by a broadpeak which is much broader than the powder peak from Fig.1�c� but roughly at the same value of q as the �111� Braggpeak.

A series of SAXS patterns from holoferritin were mea-sured at many temperatures between 10 and −25 °C for a200 mg/ml holoferritin sample in 150 mM NaCl.. A signifi-cant change in the position of the broad peak as well as thewidth and height of this peak can be seen as the temperatureis varied. This is shown in Fig. 2 where the two-dimensionaldata were integrated to yield the curves shown using the

FIG. 1. �Color online� Two-dimensional SAXS data from fer-ritin �a� and apoferritin �b�. The oscillations seen for apoferritin arewashed away in holoferritin by the presence of the iron core. �c�SAXS pattern of ferritin to which Cd salt was added to producemany small crystals. �d� Solution of ferritin frozen to −20 °C.

FIG. 2. �Color online� SAXS data at indicated temperaturesshowing the change in scattered intensity from holoferritin solutionat 200 mg/ml upon freezing and as the temperature is varied.

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program FIT2D �16�. The solution was found to freeze at �−7.5 °C as could be seen from the opaqueness of the samplebut would only melt back at �−2 °C. Considering the rela-tively small solute concentration in the sample, this largedepression of the freezing point appears to be an indicationof supercooling. It is conceivable that the presence of proteinmolecules and salt make it easier to supercool the solution,allowing the lower temperatures to be reached without icenucleation. Plenty of time was given to the temperature toequilibrate when it was changed and this difference betweenthe freezing and melting points was reproducible. The data attemperatures between −2 and −7.5 °C was collected by heat-ing the sample from a lower temperature, while the otherdata points were collected while cooling the sample from ahigher temperature. There was significant hysteresis ob-served and the direction of the change in temperature wasvery much relevant.

The presence of the peak in the scattering data indicatesthat the proteins organize differently in the frozen solutionthan they do at room temperature. The peak is seen not to bedue to the form factor of the molecules since it is not presentat room temperature. Also, the value of q at which the peaksoccur clearly indicates that it is the ferritin molecules and notice crystals which cause the peak.

From the position of the peaks, we can extract a spacingof the molecules in the aggregates that are formed. This isshown on the top panel of Fig. 3 for all the temperaturesstudied. There is a strikingly large thermal expansion. The

spacing between the molecules changes �20% over a rangeof only 25 °C. The spacing at low temperature is smallerthan the spacing of the �111� lattice planes in the fcc crystalwhich is 106 Å.

The width of the peaks gives information about the aver-age size of the individual aggregates using the Scherrer for-mula. The size is given by 2� /FWHM where FWHM is thefull width at half the maximum of the peak. This value isplotted versus temperature on the bottom panel of Fig. 3. Thevalues range between 200 and 600 Å which corresponds toclusters of 6 and 36 particles, respectively, assuming theclusters are roughly spherical.

We explain the observed behavior by a phase separationof the sample into domains which are rich in protein anddomains almost devoid of proteins, a well-known liquid-liquid phase separation �17�. When in the liquid state, thesample can be cooled below the freezing point of water dueto the high protein and salt content. Once it freezes, a net-work of ice crystals is formed. The protein molecules do nofit very well into the structure of ice and are pushed out toallow the formation of hydrogen bonds in the ice network.Voids are created in the ice and the protein molecules aretrapped in them. As the temperature is increased, the proteincontent in the ice is actually very low due to the phase sepa-ration. The melting point is then much closer to the actualmelting point of pure water. This explains the hysteresis ob-served in the freezing point temperature.

In the frozen solution, the protein molecules are muchmore concentrated because they are trapped into small vol-umes and are possibly under considerable hydrostatic pres-sure. The concentration in fcc crystals of ferritin is on theorder of 650 mg/ml. At such high concentration, the mol-ecules are very close to each other giving rise to a peak in theSAXS data. The peak position is inconsistent with simpleliquidlike ordering. Such a situation would yield a peak inintensity at a q value corresponding to a spacing equal orslightly larger than the size of the protein, i.e., 130 Å corre-sponding to a peak at q=0.048 Å−1. The presence of the peakat a higher q value indicates the presence of some level ofcrystalline ordering. Since ferritin crystallizes so readily, itbecomes more thermodynamically favorable for the mol-ecules to rearrange into a structure with some form of longrange order after phase separation. In the fcc crystal of fer-ritin, the nearest neighbor distance is 130 Å in the �110directions but the �110� reflections do not exist due to theexact cancellation in the unit cell. It is therefore clear fromthe data that there is some level of crystalline order presentin the frozen samples. The position of the peak is generallynear the expected �111� peak of the fcc crystal, at q=0.059 Å−1 suggesting a structure similar to fcc is present.

The thermal expansion occurs because of changes in theice network with changing temperature. As the temperaturedecreases, the voids in the ice where the proteins are trappedchanges. Some of the remaining water in the voids freezesand forces more proteins into smaller voids. This has theeffect of exerting pressure on the small clusters of proteins. Itis known that protein crystals are very soft compared withinorganic crystals and also ice �18–20�. A small pressure ap-plied to protein crystals by the ice will greatly affect theirstructure. This combined with the increased caging forces the

FIG. 3. �Color online� Top: Average spacing of the ferritin mol-ecules �within the clusters� versus temperature. The �111� latticespacing of fcc ferritin crystals is 106 Å. Thermal expansion of 30%is seen over the range of temperature. Bottom: Average size of theclusters obtained from inverting the width of the peaks plotted ver-sus temperature.

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proteins closer together. As the temperature is increased, thepressure is relaxed and the protein molecules start to pullapart, as observed. Increasing the average volume of thevoids in the ice by a factor of 2 would lead to an increase inmolecular spacing of 20%.

The peak position, as mentioned above, corresponds to aspacing close to the �111� fcc lattice spacing expected forferritin crystals. However, the peak is seen to move to higherq than the value for the �111� peak. This would seem toindicate that the molecules are spaced closer than the �111�crystal planes. This is surprising since the fcc ferritin crystalsare close-packed structures and therefore very little contrac-tion should be possible without compressing the moleculesthemselves. This might be an indication that the clusters arecrystalline but of a different lattice structure. It has beenhypothesized that critical nuclei that lead to the formation ofcrystals could have a different lattice structure than the finalcrystals. This would at first glance appear to be the case here.However, closer inspection and simulations discussed later inthis paper do not fully support the hypothesis that the clus-ters possess a different crystal lattice than fcc.

A. Structure factors

To better understand quantitatively the observed behavior,it is useful to examine the structure factors of the solutionsmeasured rather than the intensity. The scattered intensityfrom a solution of identical particles can be separated in twofactors, the form factor F�q� and the structure factor S�q��21�.

I�q� = �F�q�S�q��2. �1�

The form factor is the Fourier transform of the electron den-sity of one molecule. This contribution can be divided outfrom the measured intensity to obtain the structure factor,which is the Fourier transform of the spatial distribution ofthe molecules. In the dilute limit, the distribution is essen-tially a delta function because each particle scatters incoher-ently and this gives S�q�=1. This is roughly the case for theunfrozen sample in the q range measured. However, there isa large contribution to the intensity profile from S�q� whenthe apoferritin solution is frozen.

The contribution to the scattered intensity from the elec-tron density of the individual molecules, the form factor, canbe factored out if the molecules are isotropic and identical.What is left is the structure factor of the sample which de-pends in principle solely on the arrangement of the mol-ecules with no dependence on their actual shape. The formfactor was measured using a dilute solution of the proteinstudied, making the explicit assumption that at low concen-tration the structure factor was exactly equal to 1 and thescattered intensity was therefore the square of the structurefactor.

The factorization assumption in Eq. �1� that the proteinmolecules are isotropic and identical breaks down in the caseof holoferritin due to the presence of the iron cores which arenot all identical. Direct calculation of the 3D form factor ofapoferritin from the known atomic structure has shown it tobe nearly isotropic and well described by a spherical shell.

However, the iron cores from different protein molecules areall different and therefore the intensity is no longer factoriz-able. Also, it is likely that the cores themselves are not iso-tropic. They are however not expected to have preferred ori-entation within the molecule even though the residues insidethe shell are believed to play a role in the nucleation of theiron �22�.

So in summary, the form factor of the iron-loaded proteinsis not known and cannot be properly measured, leading toinaccurate measured structure factors. However, the low qpart of the structure factor below q=0.1 Å−1 is a good ap-proximation. The analysis of the structure factors of holofer-ritin is therefore restricted to the low q part.

B. Concentration dependence

In Sec. III, we suggested that the cause of the formationof the clusters is a phase separation in which the proteins areexcluded from the solution and trapped into a confinedspace. If this is so there should be a very significant differ-ence in the behavior of solutions of different protein concen-tration when frozen. We therefore repeated the same experi-ment for a few holoferritin concentrations. Figure 4 showsthe results for a series of temperatures on solutions of 100,50, and 35 mg/ml of holoferritin in 150 mM NaCl. Each ofthese sets of data was collected by cooling down to the low-est temperature shown ��−25 °C� and then gradually heat-ing the sample up until no peak could be seen any longer.

For a solution at 100 mg/ml shown in Fig. 4�a�, a singlebroad peak is formed upon cooling. However, as the tem-

FIG. 4. �Color online� Structure factors at various temperaturefor holoferritin solutions at �a� 100 mg/ml, �b� 50 mg/ml, and �c�35 mg/ml. In each case, the first temperature measured was thelowest, shown on top. As the temperature is increased, the peaks getnarrower indicating an annealing process creating larger crystals.The overall cluster size is smaller as the concentration increases asseen by the broader peaks at 100 mg/ml.

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perature is increased, this peak is seen to split into two nar-rower peaks. This indicates the formation of larger clustersas the temperature is increased. As simulations will show inSec. V, the single broad peak seen at 200 mg/ml and thelowest temperature at 100 mg/ml is in fact the combinationof the first two peaks of the face-centered cubic lattice and asthe size of the cluster is increased, they get narrower andbecome distinct peaks. Therefore, the lattice spacing isroughly constant and at a value near the expected latticespacing of 106 Å as the temperature is increased. The clus-ters, however, get larger and larger with increasing tempera-ture.

A similar behavior is observed with a solution of50 mg/ml in Fig. 4�b�. The clusters at the lowest temperatureare larger than at 100 mg/ml as indicated by the split peakand the smaller width. Again, however, as the temperature isincreased, the peaks get narrower indicating larger crystallineclusters. Multiple Bragg peaks are seen and they correspondto the expected q positions of the expected fcc lattice witha=183 Å.

Figure 4�c� shows the temperature series at 35 mg/ml.When the sample is cooled to −19 °C, distinct Bragg peaksare already present. There is, however, a shoulder on the lowq side which is reminiscent of the broad peak seen at100 mg/ml. There is a coexistence of two separate states inthe sample: small ��500 Å� clusters leading to the presenceof a broad peak and large ��0.5 �m� crystals. The distinc-tion between the characteristic structure factor of each stateand the combination of both is made clear in Fig. 5

The experiment was repeated for more protein concentra-tions below 35 mg/ml. In all cases, large crystals giving riseto large Bragg peaks start to dominate the structure factor.The small clusters are, however, still present in small numberand their contribution to the structure factor can still be seen.There is a coexistence of the two phases at many tempera-tures for certain concentrations. At 200 and 100 mg/ml, onlyone state was observed, with the small clusters growing intoslightly large ones.

The constant position of the sharp peaks indicates thatonce large crystals form, the lattice spacing is fixed to a

value near the fcc value of 106 Å for the �111� spacing. Theestimated crystal size from the Scherrer formula, i.e., thedecrease in peak width with decreasing concentration showsthat crystals get larger with decreasing protein concentration.This can be explained again by the trapping of proteins intovoids in the ice after phase separation has occurred. Afterrapid cooling, the molecules are originally trapped into acertain conformation. At high concentration, there is a lot ofcrowding and the molecules cannot reorganize at any tem-perature before melting occurs. However, at lower concen-trations, an increase in temperature provides enough energyto the system and increases the available space to allow theprotein molecules to reorganize in such a way as to producelarger crystals. This is similar to an annealing process. Themolecules have some room to move around and are nottrapped in their original configuration. Therefore, the lowerthe concentration, the easier it is for large crystals to form, tothe point that they are even seen immediately upon freezing.Also, in all cases the crystals are seen to get larger withincreasing temperature, until a certain temperature is reachedand then they are no longer seen. It seems that at lowerconcentrations, the proteins are only loosely trapped andheating the sample configuration provides enough room fordiffusion for the proteins to get over the configurational bar-rier required to get out of the trapped state. There is enoughspace available for the proteins to explore new configura-tions and rearrange into larger aggregates with better definedcrystalline order. The fact that small clusters can be annealedinto large crystals might indicate that they are a precursorstate to crystallization, possibly related to the nucleation pro-cess.

The spacing obtained from the broad structure factor peakis seen to be inversely proportional to the concentration. Thatis the peak moves to lower q with increasing concentration.This may be due to a crowding effect whereby more proteinsget trapped per void for the more concentrated solution. As-suming that the size of the voids is the same for differentconcentrations, the 200 mg/ml solution will have twice asmany proteins per void as the 100 mg/ml solution and 10times more than the 20 mg/ml solution. If we assume themolecules space-fill voids of a fixed volume independent ofthe protein concentration, the more concentrated solutionwill have a smaller spacing. It is then not surprising that thespacing corresponding to the broad peak gets larger sincethere is less crowding. The small clusters are very compress-ible compared to the large crystals which have a fixed spac-ing. The size of the clusters obtained from the width of thepeaks remains fairly constant for all concentrations below100 mg/ml at roughly 300 Å. For the lowest concentrations,the spacing starts to approach the size of the molecules at130 Å. The packing therefore resembles more a liquidlikestructure than small crystalline clusters. Evidence of liquid-like packing is seen at low concentration as well as at highertemperature. At the highest concentrations measured, the lat-tice spacing increases with temperature.

IV. APOFERRITIN RESULTS

Similar experiments were performed using solutions ofthe empty protein shell apoferritin. The signal from these

FIG. 5. �Color online� Comparison of the structure factor fromlarge crystals �black�, small clusters �blue�, and the coexistence ofthe two �red�. Sharp peaks arise from large crystals while broaderfeatures are associated with small nanoclusters.

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samples was significantly weaker and made measurements oflow concentrations difficult. Figure 6 shows the intensitymeasured from samples of apoferritin containing 50 and150 mg/ml with 100 mM NaCl. The most intense curve ineach case corresponds to the unfrozen sample. All haveBessel-function-like oscillations due to the spherical shape ofthe protein molecules. The form factor in the case of apofer-ritin is approximately given by the Fourier transform of aspherical shell with inner radius r1 and outer radius r2:

F�q� =�sin�qr1� − qr1 cos�qr1��

q3�r13 − r2

3�−

�sin�qr2� − qr2 cos�qr2��q3�r1

3 − r23�

.

�2�

A good fit to the intensity data can be obtained with Eq.�2� with a low level of polydispersity except at low q for themore concentrated solution. Comparing the two concentra-tions before freezing, one can see the appearance of a slightpeak at roughly q=0.035 Å at 150 mg/ml. This peak couldbe attributed to liquidlike ordering but careful studies byother authors indicate the presence of paracrystalline order-ing in solution �23�.

As in the case of holoferritin solutions, as the temperatureis decreased, the solution eventually freezes and a distinctchange to the SAXS pattern can be seen. At both 50 and150 mg/ml, the intensity near the origin drops and the oscil-lations from the form factor of the protein are distorted andeven canceled off. The decrease in intensity at low q indi-

cates the presence of aggregation. The total scattered inten-sity from the sample remains the same since the total numberof electrons illuminated remains the same. However, clusterformation redistributes the intensity to different values of q.The maximum at the origin gets narrower as the cluster sizeincreases and would become a delta function in the limit ofan infinite crystal. New peaks in the intensity appear wherepeaks in the structure factor are present.

When compared with the case of holoferritin, the apofer-ritin intensity curves seem to be a very complicated functionwith no clearly identifiable peak which one could interpret asa typical spacing. There is, however, a great advantage inusing the empty protein shells. They are very monodisperseand very closely isotropic. Therefore, the structure factor ob-tained is much more meaningful than in the iron-loaded pro-tein case. In the latter, the structure factor measured was onlya first order approximation valid over a small q range. In theapoferritin case, the entire structure factor curve obtainedshould be valid.

A. Structure factors

The unfrozen solution provides a good measure of themolecular form factor. The data for frozen solutions weretherefore divided by this measured curve to obtain the struc-ture factor using Eq. �1�. The derived structure factors areshown in Figs. 7�a� and 7�b� for 50 and 150 mg/ml, respec-tively. The complicated intensity curves turn into smooth

FIG. 6. �Color online� SAXS intensity from solutions containing�a� 50 mg/ml and �b� 150 mg/ml of apoferritin in 100 mM NaCl.The intensity changes significantly upon freezing indicating aggre-gation leading to a change in the structure factor.

FIG. 7. �Color online� Structure factor measured from apofer-ritin at �a� 50 mg/ml and �b� 150 mg/ml. The structure factorchanges with temperature.

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curves when divided by the proper form factor. Peaks in thestructure factor again indicate the presence of some form ofordering. The presence of multiple peaks indicates a goodlevel of long-range order.

At 150 mg/ml, the solution did not freeze until a tempera-ture lower than −9 °C was reached. The first three peaks inthe structure factor are clearly visible. One thing to notice isthe slight splitting of the first peak. The interesting aspect ofit is the fact that the lower q part of the peak has a lowerintensity than the higher q part. It is expected from the ho-loferritin data and from calculations of the diffraction froman fcc crystal that the second peak, the �200� peak of fccferritin crystals is weaker than the first peak, the �111� peak.

The structure factors for the solution at 50 mg/ml displaymore features. Most importantly, the second broad peak atq�0.12 Å−1 is split, with a sharp peak appearing at q�0.1 Å−1. The position, height and width of this peakchanges significantly with temperature, moving to lower qwith increasing temperature. Another small peak at q�0.15 Å−1 is seen for a few of the measured temperatures.

The thermal expansion measured is compared in Fig. 8with that of holoferritin. The holoferritin sample was at100 mg/ml with 150 mM NaCl while the apoferritin samplewas at 50 mg/ml with 100 mM NaCl. The difference inmass concentration is due to the heavier protein with iron.The molar concentration of both samples is the same within30%. As can be seen, the results for the two are very similar,indicating that the presence of the iron core does not play animportant role, if at all, in the aggregation mechanism. Theincrease in the molecular spacing follows the same curve forboth cases, with the absolute values differing only becausethe holoferritin sample is slightly more concentrated givingrise to a smaller spacing. As a reference, a dashed line wasdrawn at a value corresponding to the spacing of the �111�planes in the fcc crystal of ferritin. The measured spacingappear to be smaller than the crystal spacing, but as men-tioned before, this is due to the merging of the first twoBragg peaks into one broader peak.

V. CLUSTER SIMULATIONS OF STRUCTURE FACTOR

The size of the small clusters of ferritin we have observedranges from 300 to 600 Å roughly. Considering the size of

the ferritin molecules is 130 Å, this means that a cluster ofdimension 600 Å has only 4–5 molecules across, containinga total of 100 molecules or less. This total is small enoughthat one can realistically calculate exactly the structure factorof a cluster by treating it as one “supermolecule.” If weassume that there is a central molecule located at the originof real space, we can add molecules one by one and calculatethe spherically averaged form factor directly using the Debyeformula �21�

S2�q� = i

N

j

Nsin qrij

qrij, �3�

where N is the total number of ferritin molecules and rij isthe distance between molecules i and j. The value of N inour case would be limited to less than 200 making this cal-culation somewhat straightforward using a simple computerprogram. This formula gives a spherically symmetric scatter-ing functions even for non symmetric distributions of par-ticles.

A. Isotropic clusters

It is logical to start by assuming the small clusters possessa face-centered cubic structure since this is the most easilyformed crystal structure of the protein. As a first guess of thestructure of the clusters, one might assume a roughly spheri-cal aggregation, with a central molecule to which new mol-ecules attach forming an isotropic structure. Supermolecularclusters were built up starting with a central molecule locatedat the origin. Molecules were added one by one on fcc latticesites. The structure of the dimer is unique. However, thetrimer structure and most other oligomeric structure have de-generate states. Even if one limits the number of possibleconfigurations to keep the overall supermolecule roughlyspherical, there are still multiple possibilities. The first neigh-bors from the central molecule in the fcc structure are all the�110 lattice sites. It does not matter which one of the 12possibilities is chosen first since a simple rotation transformsany cluster formed into any other one. However, differentstructures are formed depending on which of the remaining�110 sites is chosen next. In general, all supermoleculesbuilt this way are degenerate. However, clusters containingonly filled shells of nearest neighbors are unique. If all the 12�110 sites are occupied, the supermolecules containing 13ferritin molecules is unique. The same goes for all otherfilled shells.

The structure factor was calculated using equation �3� forsupermolecules of 1 to 177 ferritin molecules. The number177 corresponds to a supermolecule containing the first 9shells around the center molecule, that is adding every latticepoint up to the �330 and �114 fcc points, which have thesame distance to the center molecule.

In Fig. 9, the structure factor is seen to evolve from unityfor the one central molecule to an oscillating curve for the177 molecule cluster. Only filled shell cases are shown, con-taining 1, 2, 13, 19, 43, 55, 79, 87, 135, 141, and177 molecules, corresponding to the monomer, the dimer,and filled shells up to �110, �200, �112, �220, �310, �222,

FIG. 8. �Color online� Spacing of the apoferritin molecules ver-sus temperature overlaid with the spacing from iron loaded ferritin.

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�123, �400, and ��330 and �114�, respectively. These rep-resent roughly spherical clusters of diameter 260, 368, 450,520, 581, 637, 688, 736, and 780 Å.

The structure factor from the monomer is exactly unity.The structure factor from the dimer is the sinc function. Asthe cluster size grows, broad peaks get more well defined.These peaks are at q values near the fcc Bragg peaks. Focus-ing our attention on the first peak at q�0.06 Å−1, one no-tices that as the number of protein molecules is increased,this peak gets narrower, then splits into two distinct peaksthat also get progressively narrower. This is because there aretwo Bragg peaks near q=0.06 Å−1. The �111� Bragg peak isat q=0.0591 Å−1 and the �002� peak is at q=0.0686 Å−1. Fora small cluster of 13 molecules, the diameter of the cluster is390 Å corresponding to a width of the diffraction pattern of0.016 Å−1. The two peaks are then indistinguishable. Thesame thing occurs at other q values. As the crystal grows,Bragg peaks become better defined, until they essentially be-come delta functions in the infinite limit.

The simulations shown in Fig. 9 show a good similaritywith the structure factor data obtained for holoferritin at lowq and also for apoferritin over the whole q range measured.The first peak was often measured to split with increasingtemperature as seen also in the simulation. The very rapidoscillations in the very low q part of the simulation arisesfrom the exact shape of the clusters. This part is very sensi-tive to the exact structure. It is not expected that every clusterin the sample will be identical. Instead, a weighted sum overmany of the simulated clusters is a better description of thesystem. Such a summation over a small range of sizes willaffect very little the overall structure factor at values of qabove the first minimum. The very low q part, which is oftennot even measured in our experiments would then averageout to a smooth function.

We next address the question of whether the small clusterscan be composed of other plausible structures. One such pos-sibility would be the formation of a hexagonal close-packed�hcp� structure. The hcp structure is similar to the fcc struc-ture with identical layers in the �111� plane but with a differ-

ent stacking of these layers. Similar simulations of the struc-ture factor were performed using an hcp structure. The result�not shown� clearly showed the data is inconsistent with thehcp model. Most of the Bragg peaks of fcc and hcp are thesame due to the similarity of the two structures. However,the hcp lattice gives rise to some peaks which are clearly notpresent in the data.

Also, it was mentioned above that the spacing measuredby fitting the peak position of the iron-loaded ferritin corre-sponded at low temperature to a spacing smaller than the�111� spacing. We mentioned that this might indicate a dif-ferent structure than fcc. However, close inspection of thecalculated structure factors indicates that the peak maximumfrom a small fcc supermolecule is not at the q value of the�111� Bragg peak but rather at a value of q corresponding toa spacing of �103 instead of 106 Å. This is still larger thanwhat we measure indicating that the lattice spacing is indeedcompressed from the expected bulk value.

B. Planar clusters

Work published by Yau and Vekilov presents evidencethat the nucleation of apoferritin proceeds along a planarrather than an isotropic pathway �9�. They measured directlythe structure of small clusters of apoferritin using atomicforce microscopy �AFM�. Their data indicate the formationof rod structures aggregating into a close to planar structure.Supermolecules of this type were simulated in order to de-termine if they are a good representation of our data.

Figure 10 shows simulated structure factors for those pla-nar clusters which were observed by Yau et al. They ob-served using AFM that near critical nuclei of ferritin formingin solution and falling on a substrate were made of 4 to 8rows of 4 to 7 molecules. The rows of molecules are alongthe �110 directions of the fcc crystal and are arranged in anaccordion structure. These clusters were found to be nucleinear critical in size. Even though all the molecules in theseclusters lie on fcc lattice spots, the cluster shapes are clearlydifferent from the spherical fcc cluster simulated above andwill therefore have a different scattering structure factor.Simulations were made for 1 to 12 rows of

FIG. 9. �Color online� Simulated structure factors from fcc su-permolecules made of 1, 2, 13, 19, 43, 55, 79, 87, 135, 141, and177 molecules, corresponding to the monomer, the dimer, and filledshells up to �110�, �200�, �112�, �220�, �310�, �222�, �123�, �400�,and ��330� and �114��, respectively.

FIG. 10. �Color online� Simulated structure factors from planarsupermolecules made of 5 �110 rods of 1 to 12 molecules each.

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1 to 12 molecules. Figure 10 shows the simulations for 5rows of 1 to 12 molecules.

There are significant differences between the isotropiccluster structure factors of Fig. 9 and the structure factorsfrom the planar structures. This indicates that SAXS is agood technique for distinguishing between the two even ifthey are randomly oriented. The peaks for both cases are andshould be at the same q values and get narrower with in-creasing cluster size since the position of the peaks dependson the lattice, which is fcc in both cases. However, the planarstructure has many planes of the fcc structure missing andtherefore some characteristic distances either occur less oftenor not at all. This in turn leads to different widths of thepeaks. Similarly, the size of the cluster is different in alldirections. The directions where it is larger will give rise tonarrower peaks while the peaks corresponding to the direc-tions where the cluster is small will be much broader. Thisleads to the first peak getting much narrower before it startsto split into two peaks when comparing to the isotropic clus-ter case.

The planar clusters when compared to the fcc clustersdisplay a much sharper first peak for the same number ofmolecules. For example, the cluster with 5 rows of8 molecules, for a total of 48 ferritin molecules, has a muchsharper peak at q=0.06 Å−1 than the fcc cluster with55 molecules. Also, the planar cluster simulation give rise toa sharper peak at q=0.1 Å−1 without a splitting of the firstmaximum as seen for the isotropic clusters. A quick inspec-tion of the data indicates that the first maximum is alwaysnarrower in the planar case than in the isotropic simulations.The only way an fcc cluster can yield a structure factor witha sharper first maximum is by increasing the size of the clus-ter, but this will in turn cause this first maximum to split intotwo. This may be an indication that sometimes planar clus-ters do form according to the way Yau et al. observed.

VI. FITTING OF STRUCTURE FACTORS

It is logical to assume that there is a cluster size which ismore likely than others. There could be a Gaussian distribu-tion, for example, around a central supermolecule size. Inorder to determine this central value, a fit was performed foreach structure factor measured assuming only 1 type of su-permolecule was present. A fit was performed for each modelsimulated, including spherical clusters up to 177 moleculesand planar clusters containing anywhere between 1 to 11rods of 1 to 12 molecules. The computer program kept trackof the parameters obtained for each of these fits and at theend, the supermolecular model yielding the lowest value of�2=�S�measured�−S�fit��2 was output. Thus 309 fits wereperformed on each data set and the best fit was kept as themost likely supermolecule, among all the simulations per-formed.

The fits obtained at a few temperatures on the 200 mg/mlholoferritin sample are shown in Fig. 11�a�. The fits for a100 mg/ml sample is shown in Fig. 11�b�. They are shownin the order at which they were measured from bottom totop. The width and position of the first peak is well capturedand even the secondary features are fitted. The model which

yielded the best fit shown is indicated directly next to thecurve, as well as the temperature the data was collected at.The symbols are the data while the solid curves are the fits.Some of the best fits obtained were using the planar clustermodel. This was only the case for fairly small clusters. Thisis not completely unexpected since Yau et al. only observedsmall ones and this planar structure is assumed to be only anintermediate crystallization state and is not the equilibriumlarge crystal shape. However, smaller clusters have a moregeneric structure factor with less well-defined features. Thestructure factors from the two models eventually converge asthe size gets smaller, with the dimer models being identical.There are multiple models which can be used that give adecent fit for the small clusters. Nevertheless, the multipleoccurrences where the best fitting model is a planar clusterindicates that these do indeed occur. They are, however, notthe predominant form for most of the samples measured. Thelattice spacing of the clusters fitted was found to match verywell the estimated values from just the position of the firstpeak.

The fits to the structure factors for two different samplesof apoferritin at 50 mg/ml are shown in Figs. 12�a� and12�b�. The data are shown in the order at which they weremeasured from bottom to top. As opposed to the holoferritincase, the structure factor of apoferritin samples is expected tobe valid over the whole range of q due to the small polydis-persity of the molecules. This allows us to fit more than justthe first maximum and get more information about thesample.

FIG. 11. �Color online� Fits �solid lines� to the measured struc-ture factors �symbols� at multiple temperature for �a� a 200 mg/mlholoferritin sample and �b� a 100 mg/ml sample. The temperatureas well as the model used for the fit is indicated directly next to thedata curve. The curves are offset for clarity.

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The fits obtained all indicate that the isotropic clusters arepredominant. The size of the clusters varies with tempera-ture, with the general trends noted previously, that smallclusters at low temperature can grow larger when annealednear the melting point of the sample.

In order to obtain these fits, a few free parameters otherthan the lattice spacing of the clusters were included in thefitting programs. Those were a constant and a slope value toaccount for errors in the normalization and the backgroundsubtraction in the intensity data. Also, an overall scale mul-tiplying the simulated structure factor was used to determinewhich fraction of the proteins in solution was included in theclusters. Finally, the last parameter was a damping term tothe structure factor. This damping term is the Debye-Wallerfactor �DWF� used to simulate the presence of thermal vibra-tions in the sample as well as disorder.

The fraction of proteins included in clusters or crystal-lized fraction showed that when frozen, nearly 100% of theproteins were included in a cluster but as the temperatureneared the melting point, this number started to drop, indi-cating the crystals were breaking apart. A typical value of theDWF corresponds to a root mean square displacement ofroughly 4 Å for holoferritin and 2 Å for apoferritin. The dif-ferent values are representative of the higher disorder due tothe presence of the iron core.

VII. CONCLUSION

The aggregated state formed upon freezing solutions offerritin, first seen by Kilcoyne �12�, is found to be due tocluster formation. A phase separation process is envisaged inwhich protein depleted ice surrounds voids of concentratedprotein, trapped in the ice network. The protein rich regionsmay or may not be frozen. They may still be in a liquidaqueous environment due to their high solute percentage.The phase separation explains the hysteresis of the systemcausing it to have different freezing and melting tempera-tures

Clusters possessing face centered cubic symmetry arepresent at all temperatures. At the highest temperatures, theydisintegrate into smaller fcc structures and eventually revertback to a solution. The evidence indicates the clusters breakup into smaller ones before they revert to liquidlike highlyconcentrated structures though there is some evidence of liq-uidlike packing leading to peaks in the structure factors. Thelarge lattice spacings observed at high temperatures are bet-ter explained by a concentrated liquid than a solid with anexpanded lattice. However, there is clear evidence of a largethermal expansion of the fcc lattice with increasing tempera-ture. The lattice spacing of holoferritin solutions producinglarge crystals is directly measured and shows a slight thermalexpansion. It is however the smaller structures which showthe larger thermal expansion for 100 and 200 mg/ml holof-erritin. Fits to the structure factors show that the sample con-sists of many small fcc supermolecules and the average lat-tice spacing greatly increases. This is quite interestingbecause it indicates that the fcc structure is a stable one evenwhen the protein molecules are far apart and no longer di-rectly in contact. This is reminiscent of colloidal systems inwhich crystal structures can be formed even at very low vol-ume fractions, below the fraction one would get if the col-loids were in direct contact. In charge stabilized colloidalsystems, the spacing between the particles in the crystal canbe many time the diameter of the particles. It is well knownthat the salt concentration in colloidal suspensions changesthe organization in the sample from a fluid to various crys-talline structures by screening the Coulomb interactions�24,25�. The addition of salt to the ferritin solution changesthe size of the fcc clusters formed and whether they occur atall. The ferritin proteins trapped in ice appear to behave simi-lar to colloidal particles in the sense that they have crystal-line order with a varying lattice spacing and without directcontact between nearest neighbors in the lattice.

The measured decrease in size and number of the clusterswhen approaching the melting point is consistent with previ-ous measurements of Kilcoyne et al. using small angle neu-tron scattering �12�. Their analysis was based on the charac-teristics of the very low q range where the presence of largestructures has a large effect. They did measure a few weakpeaks in the intensity which they tentatively assigned toBragg peaks from the hexagonal close-packed structure, buttheir data did not fully verify this. No measurement of theannealing process discussed above was made in their case.

The fits to the structure factors discussed were of only asingle cluster model at a time. There is no reason to expectthe sample to contain a single cluster structure. There should

FIG. 12. �Color online� Fits �solid lines� to the measured struc-ture factors �symbols� at multiple temperature for two separate50 mg/ml apoferritin sample. The temperature as well as the modelused for the fit is indicated directly next to the data curve. Thecurves are offset for clarity.

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be a range of different structures with different probabilities.Only the most likely structure was fitted for the followingreasons. First, the structure factors simulated for a singletype of clusters such as the spherical clusters is a slow vary-ing function of the number of particles. There is not muchdifference between the structure factor calculated from a su-permolecule containing 45 molecules and a supermoleculecontaining 50 molecules. Therefore, using multiple similarmodels and summing them together only slightly improvedthe fits. Furthermore, including too many models leads tomany fit parameters which created too many degrees of free-dom leading to multiple solutions. The real system probablyincludes a structure which is more likely to occur than otherswith the other structures within a range of sizes present withsome probability, including isomorphic structures whichwhere not all simulated. It proved impossible with the avail-able data to determine this range of size with accuracy.

It is also possible that different habits of the clusters arepresent. Clusters could be forming with both planar and iso-tropic structures. It again becomes tricky to allow both toexist in the fitting routine, leading to ambivalent multiplesolutions. Therefore, only the most likely structure of thesupermolecules could be determined.

Some of the fits obtained indicate the most likely structurepresent is consistent with the planar nucleation structuresmeasured by Yau and Vekilov �9�. Most of the data is, how-ever, better explained by the isotropic simulations. We there-fore conclude that isotropic nucleation is the main pathwaybut the planar pathway also occurs with a small probability.

The data clearly indicated the presence of very small clus-ters down to less than 10 molecules at early times shortlyafter the sample was cooled. As the temperature was raised,these small clusters grew into large crystals. There is clearevidence in Fig. 5 that both crystals and small clusters cancoexist, with smaller clusters appearing first and then grow-ing larger. The freezing process causes nucleation of the pro-tein molecules. These small structures with fcc ordering arestable at certain temperatures. Raising the temperature causesa change in the level of saturation of the sample that allowsthese clusters to grow. Therefore, the small supermolecules

are identified as the nuclei of ferritin at these concentrationsand temperatures. They are stable aggregates more likely togrow than to redissolve.

The fact that the peak in both the ferritin and apoferritindata shifts with temperature indicates that the contacts be-tween the proteins are fairly loose. The molecules are not indirect contact as they are in the crystal. The large expansionof the spacing as the melting point of ice is approached frombelow while the peak remains present indicates that thestructure is partially preserved but the proteins are no longerin contact. This is very reminiscent of colloidal crystalswhere the components are not directly in contact, yet arehighly organized. The lattice spacing of a colloidal crystalcan be changed without destroying the lattice by altering theconditions in the solution.

It is unclear how the results can be applied to other pro-teins. It is very likely that every protein behaves differentlywhen frozen and most may not form crystals as readily asferritin, but this is unknown. All proteins would likely showdifferent thermal compressibility of the lattice if they crys-tallize at all in this way. More studies may reveal that it maybe feasible to create small crystallites of many proteins usingthis technique. With new powerful free electron laser x-raysources such as LCLS coming online in the next few years, itmay be possible to use such small crystals for structure de-termination.

ACKNOWLEDGMENTS

This research was supported by the NSF under Grant No.DMR03-08660. The UNICAT facility at the Advanced Pho-ton Source �APS� was supported by the University of Illinoisat Urbana-Champaign, Materials Research Laboratory �U.S.DOE Contract No. DEFG02-91ER45439, the State ofIllinois-IBHE-HECA, and the NSF�, the Oak Ridge NationalLaboratory �U.S. DOE under contract with UT-BattelleLLC�, and the National Institute of Standards and Technol-ogy �U.S. Department of Commerce�. One of the authors �S.Boutet� wishes to thank the Fonds québécois de la recherchesur la nature et les technologies for its support.

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